Understanding the asymmetry in core collapse supernova explosions is pointed out by various astrophysicists as it is the key factor in determining the observational properties of the pulsars. The initial kick given by the ex- plosion to the pulsar affects its spin period and space velocity. Up to now, although the observations do not show a direct relation between the observational features of the pulsar and its space velocity, they show a clear relation between the spin period and the magnetic field strength, hence its radiation processes. In this thesis, as the method, tracing the companions of progenitors if they were in close binaries, which becomes a runaway star after the supernova explosion was chosen. Over the candidates selected in Guseinov et al (2005), the spectral types of 11 runaway candidates from 7 supernova remnants determined through analyzing their spectroscopic observations. Radial velocity determination was applied to the discovered B6V type star GSC 03156-01430 inside the supernova remnant G78.2+2.1. Also by studying the proper motion data, we compared the motion of the runaway star and the related pulsar in order to determine the asymmetry in the supernova explosion. The neutron star PSR 2021+4026 is moving with a 2-D velocity of &sim / 580 km/s with respect to the rest frame of its birth association Cyg OB9. &sim / 550 km/s more than expected in the symmetric case. Re-constructing the pre-supernova binary shows that the asymmetry in the supernova explosion does not depend on the binarity.